Optimal state feedback controller for balancing cube

• Autorzy: Kowalczyk Adam , Piotrowski Robert

Identyfikatory

DOI

10.14313/JAMRIS/3-2022/19

• Języki publikacji: EN

Abstrakty

EN

In this paper, a nonlinear balancing cube system is considered, the concept for which is based on an inverted pendulum. The main purpose of this work was the modelling and construction of a balancing cube with the synthesis of the control system. The control objectives included swing-up and stabilization of the cube on its vertex at an unstable equilibrium. Execution of the intended purpose required, first, deriving a cognitive mathematical model. It was based on the Lagrange method. Next, a mathematical model for control purposes was derived. The project of the physical model of the balancing cube was presented. A stabilization system based on a linear quadratic regulator (LQR) was developed. Moreover, a swing-up mechanism was used to bring the cube close to the upper equilibrium point. The algorithm switching condition was important to enable the correct functioning of the system. The developed control system was verified in the Matlab environment. Finally, verifying experiments and comparisons among models (mathematical and physical) were performed.

Słowa kluczowe

EN

balancing cube; control systems; linear quadratic regulator; mathematical model; physical model

• Wydawca: Łukasiewicz Industrial Research Institute for Automation and Measurements PIAP
• Czasopismo: Journal of Automation Mobile Robotics and Intelligent Systems
• Rocznik: 2022
• Tom: Vol. 16, No. 3
• Strony: 3--12
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Kowalczyk Adam

• Gdańsk University of Technology, Faculty of Electrical and Control Engineering

autor

Piotrowski Robert

• Gdańsk University of Technology, Faculty of Electrical and Control Engineering

Bibliografia

• [1] U. Adeel, K.S. Alimgeer, O. Inam, “Autonomous Dual Wheel Self Balancing Robot Based on Microcontroller”, Institute of Information Technology, Pakistan, 2013.
• [2] P. Tripathy, “Self-balancing bot using concept of inverted pendulum,” National Institute of Technology Rourkela, India, 2013.
• [3] A. Castro, “Modelling and dynamic analysis of a two-wheeled inverted-pendulum,” Georgia Institute of Technology, 2012.
• [4] B.W. Kim, B.S. Park, “Robust Control for the Segway with Unknown Control Coefficient and Model Uncertainties,” MDPI: Sensors – Open Access Journal, 2016.
• [5] K.H. Lundberg, “History of Inverted-Pendulum Systems,” IFAC Proceedings Volumes, vol. 42, no. 24, 2010, pp. 131–135.
• [6] S. Trimpe, R. D’Andrea, “The Balancing Cube – A Dynamic Sculpture as Test Bed for Distributed Estimation and Control,” IEEE Control Systems Magazine, vol. 32, no. 6, pp. 48–75 2012.
• [7] J. Mayr, F. Spanlang, H. Gattringer, “Mechatronic design of a self-balancing three-dimensional inertia wheel pendulum,” Mechatronics, vol. 5, 2015, pp. 1–10.
• [8] Z. Chen, X. Ruan, Y. Li, “Dynamic Modelling of a Cubical Robot Balancing in Its Corner,” MATEC Web of Conferences 139, 2017.
• [9] M. Gajamohan, M. Merz, I. Thommen, R. D’Andrea, “The Cubli: A Cube that can Jump Up and Balance,” Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Algarve, Portugal, Oct. 2012.
• [10] D. Morin, Introduction to Classical Mechanics with Problems and Solutions, Cambridge University Press, 2008.
• [11] K. Ogata, Modern Control Engineering, Fifth Edition, Prentice Hall, 2010.
• [12] J.P. Hespanha, “Lecture Notes on LQR/LQG Controller Design,” Knowledge Creation Diffusion Utilization, 2005.
• [13] R.M. Murray, “LQR Control,” California Institute of Technology, Control and Dynamical Systems, 2006.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).